I've been having debates with fellow writers on the merits of using dashes over commas (specifically to separate parenthetical clauses) and vice-versa. How interchangeable are these points of punctuation?

Commas and dashes are interchangeable in some instances, but each creates a different effect. Just to get us all on the same page, let’s define parenthetical clauses. These clauses provide nonessential information. You can omit this kind of clause without harming the intent of the sentence:

The Mustang, which my brother bought, was set on fire last night.

The sentence still stands without it:

The Mustang was set on fire last night.

You’ll notice I used commas to set off the parenthetical clause in the first sample sentence. Commas don’t draw attention to themselves and work well when the information in the clause is at home in the sentence in which it appears. That’s the case here.

Use a dash when you want to create emphasis:

Julie looked through the peephole to see two officers waiting for her to open the door. This eviction wasn’t supposed to happen yet—not for at least another month.

Lately Phil was so difficult—so contrary to her every suggestion—and Julie didn’t want that to ruin their trip to the zoo.

You can also opt for a dash over a comma when an appositive phrase, one that adds explanation or clarification, already includes commas:

Her closest friends—Mitchell, Fran, and Linda—bought tickets together.

Even in this instance, dashes add emphasis. If you don’t want to highlight the friends’ names, you might re-word.